Classical Tessellations and 3-Manifolds Spring 2014
Topics in Geometry; Math 24100
Instructor: Danny Calegari
MWF 12:30-1:20; Pick 22
Description of course:
This course explores the symmetries of classical tessellations --- e.g. wallpaper patterns,
friezes, crystals, especially in 2 dimensions --- and their connections to group theory and
topology, especially the topology of 3-dimensional manifolds.
(Note: because of a lack of time, we never got to
3-manifolds, so the course concentrated on the connections between groups,
geometry and topology in 2 dimensions)
Mathematics Department policy says that I should opt out of the online
evaluation process, relying instead on paper evaluations. I plan to comply with
this policy; when paper evaluation forms are available (some time in the 9th
week) I will distribute them to you in class.
There will be a midterm and a final. There will also be weekly homework. Homework is posted to this website each
Friday and is due at the start of class the following Friday. Late homework will not be accepted.
- Homework 1, due Friday, April 11; also lozenge.eps and dots_array.eps
- Homework 2, due Friday, April 18; also cubic_lattices.eps
- Homework 3, due Friday, April 25; also triple_point.eps and doubletorus.eps (this file was produced with wireframe)
- Homework 4, due Friday, May 2; also spiral_tiling.eps and paper_dolls.eps
- Midterm was given out in class Friday, May 2; also sketch solutions by Yan Mary He
- Homework 5, due Friday, May 16; also V_minus_one.eps
- Homework 6, due Friday, May 23; also Farey.eps
- Homework 7, due Friday, May 30; also right_angled_pentagons.eps
- Final was given out in class Friday, May 30.
The skeleton of the syllabus is the following.
- Introduction to Tessellations
- Continuous and discrete groups
- Euclidean Wallpaper groups
- Spherical and hyperbolic geometry
- Surfaces and circle bundles
- Seifert fibered spaces
Notes from class and downloads:
The textbook for the class is:
Bill Casselman's online copy of Mathematical Illustrations
, an introduction to programming in postscript, is here